$$ \begin{aligned} x+\frac{3}{10} &= \frac{x}{7}&& \text{multiply ALL terms by } \color{blue}{ 70 }. \\[1 em]70x+70\cdot\frac{3}{10} &= 70 \cdot \frac{x}{7}&& \text{cancel out the denominators} \\[1 em]70x+21 &= 10x&& \text{move the $ \color{blue}{ 10x } $ to the left side and $ \color{blue}{ 21 }$ to the right} \\[1 em]70x-10x &= -21&& \text{simplify left side} \\[1 em]60x &= -21&& \text{ divide both sides by $ 60 $ } \\[1 em]x &= -\frac{21}{60}&& \\[1 em]x &= -\frac{7}{20}&& \\[1 em] \end{aligned} $$

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